The weights in kilograms of 11 bags of sugar and 7 bags of flour are as follows:
Sugar: 1.961, 1.983, 2.008, 2.014, 1.968, 1.994, 2.011, 2.017, 1.977, 1.984, 1.989
Flour: 1.945, 1.962, 1.949, 1.977, 1.964, 1.941, 1.953
(i) Represent this information on a back-to-back stem-and-leaf diagram with sugar on the left-hand side.
(ii) Find the median and interquartile range of the weights of the bags of sugar.
Solution
(i) To create a back-to-back stem-and-leaf diagram, we use the integer part of the weights as the stem and the decimal part as the leaves.
| sugar |
|
flour |
|
194 |
1
5
9
|
|
195 |
3
|
|
8
1
|
196 |
2
4
|
|
7
|
197 |
7
|
|
9
4
3
|
198 |
|
|
4
|
199 |
|
|
8
|
200 |
|
|
7
4
1
|
201 |
|
Key: \( 1 \mid 196 \mid 2 \) means \( 1.961 \) kg for sugar and \( 1.962 \) kg for flour.
(ii) To find the median of the sugar weights, we arrange them in order: 1.961, 1.968, 1.977, 1.983, 1.984, 1.989, 1.994, 2.008, 2.011, 2.014, 2.017.
The median is the middle value: 1.989 kg.
To find the interquartile range, we find the lower quartile (LQ) and upper quartile (UQ).
LQ is the median of the first half: 1.977 kg.
UQ is the median of the second half: 2.011 kg.
\(Interquartile Range = UQ - LQ = 2.011 - 1.977 = 0.034 kg.\)
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